Question

If the per unit profit associated with producing the standard glove were to increase by $3 a pair, what would the impact be on the total profit? Obje ctive Cell (Max) Original Value Final Value Cell Name $B54 Obje ctive Function (Maxim ize Profit) 218 Variable Cells Integer 18 Contin 16 Contin Original Value Final Value Cell Name $B$1 X1(#of standard gloves) $852 X2(#of deluxe gloves) Constraints Cell Cell Value Formula Status Slack Name $B$8 1) Constraint#1 (le ather cutting hours) LHS $B59 2) Constraint #2 (finishing hours) LHS $B$10 3) Constraint #3 (packag ing hours) LHS Not Binding Binding 100 $8$10$C$10 Binding 78 SBS8-SC$8 60 $859SC$9 12 riable Cells Final Reduced Objective Allowable Allowable Cell Value Cost Coefficient Increase Decrease Name $8$1 X1 (#of standard gloves) $B$2 X2 (# of de luxe gloves) 5 5.666666667 18 0 1 16 8 2 4.25 nstraints Final Shadow Constraint Allowable Allowable R.H. Side Cell Value Price Increase Decre ase Name $B$8 1) Constraint#1(leather cutting hours) LHS $B$9 2) Constraint #2 (finishing hours) UHS $B$10 3) Constraint #3 (packaging hours) LHS 78 90 1E+30 12 60 6.666666667 60 0.8 22.5 100 17 100 60 40 Total profit would increase by $18 Total profit would increase by $54 The optimal solution will change, but we cannot tell exactly how the solution changes or what the profit will be unless we reformulate the LP and r dre-solve it Total profit would increase by $3 None of the above If the per unit profit associated with each pair of standard gloves is reduced by $2, what is the impact on the optimal solution and on the total profit? Obje ctive Cell (Max) Cell Original Value Final Value Name $B$4 Objective Function (Maxim ize Profit) 0 218 Variable Cells Name $B$1 X1(#of standard gloves) $B$2 X2(#of deluxe gloves) Original Value Final Value Cell Integer 18 Cont in 16 Cont in Constraints Cell Cell Value Formula Slack Name Status $B$8 1) Constraint#1 (le ather cutting hours) LHS $B$9 2) Constraint #2 (finishing hours) LHS $B$10 3) Constraint #3 (packag ing hours) LHS 78 $B$8-SC$8 60 $B$9 $C$9 Binding 100 SB$10-$C$10 Binding Not Binding 12 riable Cells Final Reduced Obje ctive Allowable Allowable Cell Value Cost Coefficient Name Increase Decrease $B$1 X1 (#of standard gloves) $B$2 X2 (# of deluxe gloves) 5 5.666666667 18 0 1 8 16 0 2 4.25 nstraints Final Shadow Constraint Allowable Allowable R.H. Side Increase Decrease Cell Value Price Name $B $8 1) Constraint1 (le ather cutting hours) LHS $B$9 2) Constraint #2 (finishing hours) LHS $B$10 3) Constraint #3 (packaging hours) LHS 78 0 90 60 6.666666667 100 1E+30 12 60 22,5 0.8 60 100 1.7 40 The optimal solution will change, but profit will remain the same The change is outside of the ROO, so we must reformulate and re-solve the LP to answer the question There is no impact on the optimal solution, but profit will decrease by $36 There is no impact on the optimal solution, but profit will decrease by $2 None of the above olo

Answer 1

1)
coefficient of X1(standard glove) = 5

allowable increase = 5.6666
since 3 < 5.66666
optimal solution won't change
hence

profit will increase by 18 * 3 = 54

option B)

2)
allowable decrease is 1
2 is outside allowable decrease
hence we can't comment

option B) is correct

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